Does AI rely on determinism?
I'm going to assume that by free will, you mean something like the philosophical concept of libertarian free will, which is defended by philosophers like Robert Kane. In Libertarian Free Will, individuals have some capability to make choices about their actions. The classic way to argue this is by assuming some kind of spirit-stuff (e.g. a soul) that exists outside the material world, and that this spirit-stuff constitutes the consciousness of a person. Kane tries some mental gymnastics to avoid this, but then concedes something like it in a footnote. I'm not aware of any serious work that doesn't make some kind of non-physical assumption to justify this view. If someone can point at one, I'll update the answer.

By determinism, I'm going to assume you mean the usual notion of philosophical determinism: since people's decisions depend on what happened in the past, and where they are in the present, they don't really have a choice in any meaningful sense. Philosopher's like Dennett adopt a slightly softer view (compatibilism, essentially: you don't get to make big choices, but you do get to make small ones). Appeals to Quantum Mechanics are common to justify that view. In this context, free action means something more like "did something we couldn't predict exactly". An example might be: you are pre-destined to put a can of campbell's brand tomato soup in your shopping cart, but "make a choice" about exactly which of the dozens of cans you will put in. Since small choices can have large impacts (maybe that can will give you food poisoning, and the others wouldn't), this can make all sorts of things impossible to predict exactly. 

I think most AI researchers don't worry too much about these issues, but Turing actually addresses them in his paper right at the start of the field, Computing Machinary and Intelligence. The deterministic/compatibilist view point is introduced as Lady Lovelace's objection: Computers only know how to do what we tell them to, so they can't be called intelligence.

Turing's counterargument uses two prongs. First, Turing notes that computers can probably be made to learn (he was right!). If they can learn, they can do things that we don't expect, just like children do. Second, Turing notes that computers already do all sorts of things we don't expect: they have bugs. Anytime a computer exhibits a bug, it did something that was unexpected. Since we cannot generally rule out bugs in programs, computers will always do surprising things. Therefore, computers satisfy the deterministic notion of free will.

Turing also addresses the libertarian notion of free will, which is part of what he calls the "Theological Objection". The objection is that intelligence requires some kind of divine spark (like free will). Turing argues that we can't detect sparks like this right now (he actually thought we would be able to one day, and spent a lot of time looking at supernatural phenomena too). However, there's no reason to suppose that computers with the right programs won't be endowed with them. A divine creator could decide that anytime you build something brain-like, it gets a spark. If we build a program that's brain-like, maybe it gets a spark too. In the absence of some way to detect souls, it seems like we ought to just agree to treat things that seem intelligent as though they had these souls, since otherwise we don't have a really clear way to decide who is and isn't intelligent. The only remaining way is to say "only things made of human meat have souls and are intelligent". While a lot of people do actually say things like this (e.g. animals have no souls), this is a pretty arbitrary view, and I think there's no hope arguing against it. Turing suggests the "Anthropic Principal": we shouldn't assume that we're special, because the earth isn't in a special place in the galaxy, or in the universe, and we have pretty compelling evidence that we're an evolved version of other animals around us, but some groups (e.g. biblical literalists) find this unconvincing.